Stochastic Processes: Math 229B
Spring 2004, TTh 11:10-12:30 in Surge 275
Announcements
Homework
- Homework 6, due May 20.
- Chapter 7: 4, 18.
- Chapter 8: 1, 3, 4.
- Homework 5, due May 13.
- Homework 4, due May 6.
- Chapter 5: 17.
- Chapter 7: 3, 6, 10, 15.
- Homework 3, due April 29.
- Chapter 5: 4, 6, 7, 11, 12.
- Homework 2, due April 22.
- Chapter 4: 1, 5, 7, 12, 13, 14.
- Homework 1, due April 15.
- Chapter 2: 6, 9, 16, 17.
- Chapter 3: 2, 6, 7, 14.
Syllabus
Professor: Michael Anshelevich, 250 Surge Building.
Office hours: TTh 9:30-10:30 am, W 9-10 am.
Text: Bernt Øksendal, "Stochastic Differential Equations," 6th edition, Springer Verlag, 2003.
Prerequisites: Knowledge of measure-theory based probability is essential. Since Math 229A was taught in the fall, we will review the background (Chapter 2 of the textbook) in the beginning of the course. For people who haven't taken Math 229A, familiarity with the notion of stochastic process and basic properties of the Brownian motion will make the first weeks much more manageable.
Topics:
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Background on Brownian motion (Chapter 2).
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Itô integrals (Chapter 3).
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Itô formula: change-of-variable formula for stochastic integrals (Chapter 4).
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Stochastic differential equations (Chapter 5).
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Diffusions (Chapters 7,8).
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Filtering and other applications will be touched upon, time permitting.
Final project: The project can be based on a book chapter, a paper, or contain new material, and should be on a topic of interest to the student which is also related to the content of the course. Student selections are most welcome; the instructor will provide a number of suggestions, and the later chapters of the textbook contain a number of possibilities. Timeline:
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topic choice and preliminary bibliography due: April 13 (third week),
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first draft due: May 11 (seventh week),
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final version due: June 3 (tenth week),
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oral presentation: June 8 (finals' week).
Homework: weekly, due Thursdays in class. No late homework will be accepted; the lowest score will be dropped. You are encouraged to work together, but you must each turn in your own work.
Grading: Homework 50%, final project 50%.
Other important dates: April 9 (last day to add or drop a course), May 7 (last day to withdraw from a course).
Students with disabilities: Please come talk to me no later than the first week of classes.